"Does a set of all sets contain itself?" is NOT a paradox.

[Arch-Tau]

Mathematically speaking, every set is a subset of itself (ACA), meaning that every set contains itself.

[Turambar]

Originally posted by Fallschirmjag3R:

Sigh. Pinhead's determined to get his way. I (most likely) will not reply to this discussion again.

A Set of All Sets contains itself because a set of all sets contains all existing sets.

"This sentence is false" is not a paradox either, because nothing would change it from being false. There is nothing to make it true, and it would always be false; hense it has no counter-arguement, which is necessary for paradoxes. Easily why neither GLaDOS nor Wheatley got fried during being exposed to it.

"This sentence is true" is not a paradox either, since nothing exists to make it false. It has no counter-arguement.

A paradox is defined by something that has an answer that is not logically acceptable. A counter-arguement is required to get an answer.

¬¬

[jackik]

phi always contains itself, just like every other set in this world.(asfar as i understood)
and guys . . . define what your working with cause else you're all talking ♥♥♥♥♥♥♥♥(stuff with not much meaning(no real information(sorry))).
what is a hairdresser? it's only PART of a person. the individual part of that particular human may or may not cut his hair. if you think different then say WHAT it is.
"all thos, and those only" is not a paradox because what this means is 'all of those, and only those' meaning EXACTLY THE SAME THING. a paradox is something that cannot be properly defined with given logic and requires another logic to function. this is how i interpret this.
"this statement is false" can be false, not true, incorrect(because it isn't right) or it is halftrue. Paradoxes are not hings that are impossible or "loop back on themselves" but rather things that require new logic to be sustained, may that be aplicable on reality or not. BTW thats not even about sets anymore at all.
getting back to set said set.
think about an invisible non physical box with an apple and a bannana inside. are the apple and the bannana inside the box? yes, so all of the elements of BOX are part of BOX so you could say that BOX is a subset of BOX but that wouldn't give you any information of BOX apart from that it isn't one of those Russels sets where R/=R. it is important that the box itself is completely nonphysical and the apple and the bannana could my myrads of light years apart as well as years and what ever more.
please corerct me if im wrong.

[Turambar]

Mankind is doomed

[Nephilim]

I am pretty sure reality does not allow paradoxes to exist. All the ones I have heard seem to be nothing more than a play on words.

[Turambar]

Originally posted by Rock Ingersol:

I am pretty sure reality does not allow paradoxes to exist. All the ones I have heard seem to be nothing more than a play on words.

Reality allows them, but these from portal 2 are just, like you said in a very clever way, nothing more than a play on words, that shows mistakes in some logic methods, when using the language to express ideas.

[jackik]

that is what i meant that paradoxes often aren't paradoxes

[eeloocraft113]

This paradox can be considered to be a case of nonfinite russian nesting dolls inside each other.
Since the number is nonfinite, the event can not be expressed and is therefore: a paradox.

[Patrick]

It's not asking "What would a set of all sets contain if it contained itself"? It's asking, DOES a set of all sets contain itself, in which case the answer is "yes!". Paradox resolved via grammar.

[Mavi]

https://en.wikipedia.org/wiki/Russell%27s_paradox

[Puggler the Punk Rock Juggler]

a set of sets contains a set of sets contains a set of sets contains a set of sets contains a set of sets contains a set of sets contains a set of sets contains a set of sets contains a set of sets contains a set of sets contains a set of sets contains a set of sets contains a set of sets contains a set of sets contains a set of sets contains a set of sets


thank youf or coming to my ted talk